Surface codes: Towards practical large-scale quantum computation

Surface codes: Towards practical large-scale quantum computation

October 26, 2012 | Austin G. Fowler, Matteo Mariantoni, John M. Martinis and Andrew N. Cleland
This article provides an introduction to surface code quantum computing, focusing on its practical aspects for large-scale quantum computation. The authors estimate the size and speed of a surface code quantum computer and introduce the concept of stabilizers, which are used to detect and correct errors in the quantum state. They describe how logical qubits are formed in the surface code array and provide numerical estimates of their fault-tolerance. The article outlines the physical movement of logical qubits, the construction of qubit braid transformations, and the equivalence of a braid between two logical qubits to a controlled-NOT gate. Single-qubit Hadamard, $\hat{S}$, and $\hat{T}$ operators are also discussed, completing the set of required gates for a universal quantum computer. The authors conclude by briefly discussing physical implementations of the surface code and providing supplementary information in appendices.This article provides an introduction to surface code quantum computing, focusing on its practical aspects for large-scale quantum computation. The authors estimate the size and speed of a surface code quantum computer and introduce the concept of stabilizers, which are used to detect and correct errors in the quantum state. They describe how logical qubits are formed in the surface code array and provide numerical estimates of their fault-tolerance. The article outlines the physical movement of logical qubits, the construction of qubit braid transformations, and the equivalence of a braid between two logical qubits to a controlled-NOT gate. Single-qubit Hadamard, $\hat{S}$, and $\hat{T}$ operators are also discussed, completing the set of required gates for a universal quantum computer. The authors conclude by briefly discussing physical implementations of the surface code and providing supplementary information in appendices.
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